Question: Solve for $x$ and $y$ using elimination. $\begin{align*}-9x-3y &= -5 \\ -7x-y &= 5\end{align*}$
We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-1$ and the bottom equation by $3$ $\begin{align*}9x+3y &= 5\\ -21x-3y &= 15\end{align*}$ Add the top and bottom equations. $-12x = 20$ Divide both sides by $-12$ and reduce as necessary. $x = -\dfrac{5}{3}$ Substitute $-\dfrac{5}{3}$ for $x$ in the top equation. $-9( -\dfrac{5}{3})-3y = -5$ $15-3y = -5$ $-3y = -20$ $y = \dfrac{20}{3}$ The solution is $\enspace x = -\dfrac{5}{3}, \enspace y = \dfrac{20}{3}$.